Multiplication and Division of Complex Numbers in Modulus-Argument Form

This GeoGebra example dynamically visualizes the rules for multiplying and dividing complex numbers in modulus-argument (polar) form. The core mathematical concept is the trigonometric representation of complex numbers: when multiplying, moduli are multiplied and arguments are added; when dividing, moduli are divided and arguments are subtracted. The construction uses commands such as Intersect to create intersection points, Segment for line segments, Angle to mark arguments, SurdText and FractionText to display exact radical and fractional results, and If for conditional logic. Key objects include parameters r_1, θ_1, r_2, θ_2, and complex points z_1, z_2, z_3, z_4, allowing users to adjust moduli and arguments via sliders or inputs to observe the geometric positions of products and quotients. Suitable for high school or early university students learning complex number operations, and for teachers demonstrating the geometric meaning of complex multiplication and division in polar coordinates.